Analysis and Design of Asynchronous Transfer Lines as a series of G/G/m queues - PowerPoint PPT Presentation

Analysis and Design of Asynchronous Transfer Lines as a series of G/G/m queues. Topics. The negative impact of variability in the operation of Asynchronous Transfer Lines Modeling the Asynchronous Transfer Line as a series of G/G/m queues Modeling the impact of various operational detractors

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The variability experienced at a certain station propagates to the downstream part of the line due to the fact that the arrivals at a downstream station are determined by the departures of its neighboring upstream station.

The intensity of the propagated variability is modulated by the utilization of the station under consideration.

In general, a highly utilized station propagates the variability experienced in the job processing times, but attenuates the variability experienced in the job inter-arrival times.

For a station with variable job inter-arrival and/or processing times, utilization must be strictly less than one in order to attain stable operation.

Furthermore, expected cycle times and WIP grow to very large values as u1.0.

Expected cycle times and WIP can also grow large due to high values of caand/or ce; i.e., extensive variability in the job inter-arrival and/or processing times has a negative impact on the performance of the line.

In case that the job inter-arrival times are exponentially distributed, ca=1.0, and the resulting expression for CTqis exact (a result known as the Pollaczek-Kintchine formula).

The expression for cd2characterizes the propagation of the station variability to the downstream part of the line, and it quantifies the dependence of this propagation upon the station utilization.

X = random variable modeling the natural processing time, following a general distribution.

to = E[X]; o2=Var[X]; co=o / to .

NS = average number of parts processed between two consecutive setups

It is also assumed that the number of parts between two consecutive setups follows a geometric distribution, which when combined with the previous bullet, it implies that probability for a setup after any given job = 1/ NS.

Z = random variable modeling the duration of a setup

tS = E[Z]; S2 = Var[Z]

S = random variable modeling the setup time experienced by any given job =

Need to design a new 4-station assembly line for circuit board assembly.

The technology options for the four stations are tabulated below (each option defines the processing rate in pieces per hour, the CV of the effective processing time, and the cost per equipment unit in thousands of dollars).